论文标题
Serrin问题的稳定性和Alexandroff的扭曲产品歧管定理的稳定性
Stability for Serrin's problem and Alexandroff's theorem in warped product manifolds
论文作者
论文摘要
我们证明了来自几何部分微分方程的几个结果的定量版本。首先，我们获得了Serrin在太空形式中的过度确定问题的双重稳定性定理。其次，我们证明了Brendle的Heintze-Karcher不平等的稳定性定理，分别在一类扭曲的产品空间中恒定平均曲率分类。关键工具是第一作者最近在其较小的无可怜的黑森州的范围内开发稳定性的稳定性。
We prove quantitative versions for several results from geometric partial differential equations. Firstly, we obtain a double stability theorem for Serrin's overdetermined problem in spaceforms. Secondly, we prove stability theorems for Brendle's Heintze-Karcher inequality respectively constant mean curvature classification in a class of warped product spaces. The key tool is the first author's recent development of stability for level sets of a function under smallness of the traceless Hessian thereof.
